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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26. 相似文献
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This paper concerns a Markov operator T on a space L1, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:
- a the existence of invariant probabilitydensities (IPDs)
- b the existence of strictly positive IPDs,and
- c the existence and uniqueness of IPDs.
- b the existence of strictly positive IPDs,and
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J.B. Bronzan 《Nuclear Physics B》1978,134(2):261-268
We study reggeon quantum mechanics when four-reggeon couplings are present as well as the conventional three-reggeon coupling. We show that as the reggeon intercept is increased an infinite number of states pass through energy zero. We give the values of the intercepts at which states pass through zero, construct the states explicitly, and tell how fast their energy changes with intercept. We show that these higher states do not interfere with the construction of spin models. However, no spin model is possible if the one-reggeon ? three-reggeon coupling is non-zero. 相似文献